Geographical Embedding of Scale-Free Networks

A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of scale-free networks embedded by the suggested algorithm are studied both analytically and through simulations. Our findings indicate dramatic changes in the embedded networks, in comparison to their off-lattice counterparts, and call into question the applicability of off-lattice scale-free models to realistic, everyday-life networks

Achieving Good Angular Resolution in 3D Arc Diagrams

We study a three-dimensional analogue to the well-known graph visualization approach known as arc diagrams. We provide several algorithms that achieve good angular resolution for 3D arc diagrams, even for cases when the arcs must project to a given 2D straight-line drawing of the input graph. Our methods make use of various graph coloring algorithms, including an algorithm for a new coloring problem, which we call localized edge coloring.Comment: 12 pages, 5 figures; to appear at the 21st International Symposium on Graph Drawing (GD 2013

A quantitative taxonomy of human hand grasps

Background: A proper modeling of human grasping and of hand movements is fundamental for robotics, prosthetics, physiology and rehabilitation. The taxonomies of hand grasps that have been proposed in scientific literature so far are based on qualitative analyses of the movements and thus they are usually not quantitatively justified. Methods: This paper presents to the best of our knowledge the first quantitative taxonomy of hand grasps based on biomedical data measurements. The taxonomy is based on electromyography and kinematic data recorded from 40 healthy subjects performing 20 unique hand grasps. For each subject, a set of hierarchical trees are computed for several signal features. Afterwards, the trees are combined, first into modality-specific (i.e. muscular and kinematic) taxonomies of hand grasps and then into a general quantitative taxonomy of hand movements. The modality-specific taxonomies provide similar results despite describing different parameters of hand movements, one being muscular and the other kinematic. Results: The general taxonomy merges the kinematic and muscular description into a comprehensive hierarchical structure. The obtained results clarify what has been proposed in the literature so far and they partially confirm the qualitative parameters used to create previous taxonomies of hand grasps. According to the results, hand movements can be divided into five movement categories defined based on the overall grasp shape, finger positioning and muscular activation. Part of the results appears qualitatively in accordance with previous results describing kinematic hand grasping synergies. Conclusions: The taxonomy of hand grasps proposed in this paper clarifies with quantitative measurements what has been proposed in the field on a qualitative basis, thus having a potential impact on several scientific fields

From rubber bands to rational maps: A research report

This research report outlines work, partially joint with Jeremy Kahn and Kevin Pilgrim, which gives parallel theories of elastic graphs and conformal surfaces with boundary. One one hand, this lets us tell when one rubber band network is looser than another, and on the other hand tell when one conformal surface embeds in another. We apply this to give a new characterization of hyperbolic critically finite rational maps among branched self-coverings of the sphere, by a positive criterion: a branched covering is equivalent to a hyperbolic rational map if and only if there is an elastic graph with a particular "self-embedding" property. This complements the earlier negative criterion of W. Thurston.Comment: 52 pages, numerous figures. v2: New example